Reproduction:

config WindowManager Background Wallpaper /res/wallpapers/grid.png
config WindowManager Background Wallpaper /res/wallpapers/tile.png

The following patch makes this bug easier to watch:

diff --git a/Userland/Libraries/LibConfig/Client.cpp b/Userland/Libraries/LibConfig/Client.cpp
index 3394d22b58..4251bc74e2 100644
--- a/Userland/Libraries/LibConfig/Client.cpp
+++ b/Userland/Libraries/LibConfig/Client.cpp
@@ -77,6 +77,7 @@ void Client::remove_key(StringView domain, StringView group, StringView key)
 
 void Client::notify_changed_string_value(String const& domain, String const& group, String const& key, String const& value)
 {
+    dbgln("{} was notified of a change for {}::{}::{}", this, domain, group, key);
     Listener::for_each([&](auto& listener) {
         listener.config_string_did_change(domain, group, key, value);
     });
diff --git a/Userland/Services/ConfigServer/ClientConnection.cpp b/Userland/Services/ConfigServer/ClientConnection.cpp
index d52e2bf237..115a8ef2df 100644
--- a/Userland/Services/ConfigServer/ClientConnection.cpp
+++ b/Userland/Services/ConfigServer/ClientConnection.cpp
@@ -207,6 +207,7 @@ void ClientConnection::write_string_value(String const& domain, String const& gr
     start_or_restart_sync_timer();
 
     for_each_monitoring_connection(domain, this, [&domain, &group, &key, &value](ClientConnection& connection) {
+        dbgln("Notifying {} of change", &connection);
         connection.async_notify_changed_string_value(domain, group, key, value);
     });
 }

Example output:

17.122 ConfigServer(9:9): Notifying 0x011a1020 of change
17.122 ConfigServer(9:9): Syncing 1 dirty domains to disk
17.130 FileManager (Desktop)(23:23): 0x02081820 was notified of a change for WindowManager::Background::Wallpaper
17.282 [#0 SyncTask(3:3)]: Ext2FS: Flushed 4 blocks to disk
18.495 ConfigServer(9:9): Notifying 0x011a1020 of change
18.500 ConfigServer(9:9): Syncing 1 dirty domains to disk
18.500 FileManager (Desktop)(23:23): 0x02081820 was notified of a change for WindowManager::Background::Wallpaper
18.750 FileManager (Desktop)(23:23): 0x02081820 was notified of a change for WindowManager::Background::Wallpaper
18.961 FileManager (Desktop)(23:23): 0x02081820 was notified of a change for WindowManager::Background::Wallpaper
19.208 FileManager (Desktop)(23:23): 0x02081820 was notified of a change for WindowManager::Background::Wallpaper
19.391 [#0 SyncTask(3:3)]: Ext2FS: Flushed 4 blocks to disk
19.451 FileManager (Desktop)(23:23): 0x02081820 was notified of a change for WindowManager::Background::Wallpaper
19.698 FileManager (Desktop)(23:23): 0x02081820 was notified of a change for WindowManager::Background::Wallpaper
19.917 FileManager (Desktop)(23:23): 0x02081820 was notified of a change for WindowManager::Background::Wallpaper

Result:
First run of first command will result as expected
First run of second command will result as expected
Additional runs of first command will cause the client to be notified 7 times (exactly). however, the server only says it notifies that client once.
Additional runs of the second command will continue to result as expected.

The logs have a short delay between them. Inverting the command order will make this delay disappear. I assume gird.png takes slightly longer to load into a bitmap than tile.png.